SMOS L2 OS ATBD - ARGANS

93
ICM-CSIC
LOCEAN/SA/CETP
IFREMER
SMOS L2 OS
Algorithm Theoretical
Baseline Document
Doc: SO-TN-ARG-GS-0007
Issue: 3 Rev: 9
Date: 25 January 2013
Page: 93
the bubble's packing coefficient, d is the foam layer thickness, f a is the void fraction beneath
the foam layer, and finally, SSS and SST are the sea surface salinity and temperature
respectively.
4.5.1.3. Foam coverage Model
In [13], it was shown that the fractional sea surface covered by foam-layers with thicknesses
between h and h+dh at wind speed WS, namely, the term F(WS,h)dh in Equation (1), can be
decomposed as follows:
dF(WS,h)=F(WS,h)dh= dFc(WS,h)+ dFs(WS,h) (13)
where dFc(WS,h) and dFs(WS,h) are the contributions to the coverage of actively breaking
crests or active foam and of the passive foam, or static-foam formations (see [7] for detailed
terminology), respectively.
The model which is used for these two terms is a modified form of that described in detail in
[13], where the following empirical expression for dFc(WS,h) was derived:
5
3 4.
48 h ( cT c
)
2. 9 10
WS
h e dh
e
dF ( WS,
h)
(14)
c
where WS is the 10 meter height wind speed, c and c are numerical constants and is the
air-sea temperature difference. Instead of using this form directly, however, we begin with
empirical distribution functions for foam-generating breaker length per unit area per unit
breaker speed interval as derived in [13] and then generalize these equations to accommodate
improvement in the foam coverage distributions.
The breaker length distribution function is a modified form of that derived from
measurements of Melville and Matusov (2002),
~ WS
(
WS,
c)
A
3.
310
10
3
4
~ c
.
64B
WS
e
where A ~ and B ~ are constants to be specified. This distribution function differs from the
empirical form of Melville and Matusov (2002) in that the exponent is a function of wave age
rather than breaker phase speed.
Using the preceding formulation of the crest length distribution function, we can write the
crest and static foam incremental coverages in terms of wind speed and breaker phase speed
as
2
dFc
( WS,
c)
g
and
1 2
( s s )
( , )
T
a
c WS c dc e
2a
2 2 ( sT
s
)
dFs
( WS,
c)
c (
WS,
c)
dc e
g
,